AN APPROXIMATION-THEORY FOR THE IDENTIFICATION OF NONLINEAR DISTRIBUTED PARAMETER-SYSTEMS

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators are treated. Convergence of Galerkin approximations and the corresponding solutions of finite-dimensional approximating identification problems to a solution of the original infinite-dimensional identification problem is demonstrated, using the theory of nonlinear evolution systems and a nonlinear analogue of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.